The absolute square of a complex number , also known as the squared norm, is defined as
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(1) |
where denotes the complex conjugate of and is the complex modulus.
If the complex number is written , with and real, then the absolute square can be written
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(2) |
If is a real number, then (1) simplifies to
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(3) |
An absolute square can be computed in terms of and using the Wolfram Language command ComplexExpand[Abs[z]^2, TargetFunctions -> Conjugate].
An important identity involving the absolute square is given by
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(4) | |||
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(5) | |||
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(6) |
If , then (6) becomes
If , and , then
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(9) |
Finally,
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(10) | |||
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(11) | |||
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(12) |